In another hand, if we want to construct a bilinear map then we pick up a pair of covectors and then we manufacture

defined via

It is also know that for finite dimensional vector spaces the tensor of rank one are the elements of
and its dual space

In the multi-indexed versions tensors are expressions like ,
, , which
actualy are the components of tensors and are in nature scalars or scalar functions. In the multi-indexed
version tensor are arrays of quantities that obeys certain rules of transformations when we change systems of coordinates.